X^2-22x=-23

Solution for X^2-22x=-23 equation:

X^2-22X=-23

We move all terms to the left:

X^2-22X-(-23)=0

We add all the numbers together, and all the variables

X^2-22X+23=0

a = 1; b = -22; c = +23;
Δ = b2-4ac
Δ = -222-4·1·23
Δ = 392
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-14\sqrt{2}}{2*1}=\frac{22-14\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+14\sqrt{2}}{2*1}=\frac{22+14\sqrt{2}}{2}
$